Logarithmic Functions: Intro & Graphing

TS: Making decisions after reflection and review

Warm-Up

1) log416 = 2 is the logarithmic form of 4░ = 16

2) 34 = 81 is the exponential form of log ░ ░ = 4

3) log464 =

4) log2 ¼ =

Definition of a Logarithmic Function (p.274)

For x > 0, a > 0 and a ≠ 1, y = logax if and only if x = ay

Where f(x) = logax is called the logarithmic function with base a.

Properties of Logarithms (p. 274)1) loga1 = 0 because a0 = 1

2) logaa = 1 because a1 = a

3) logaax = x and alogax = x. (Inverse Property)

4) If logax = logay, then x = y. (One-to-One Property)

Using the Definition to Convert between forms

Write each in Write each in

exponential form logarithmic form

1) log3y = -4 1) 2x = 15

2) ln b = a 2) e3 = y

3) log 15 = x 3) 103 = 1000

Evaluate or Solve each logarithmic expression or equation

1) log71/49 Solve for x:

2) log168 1) log2x = log28

3) log0.001

4) log√28 2) log4x = -2

*5) log345

*6) ln 5 3) 3log3x = 7

Logarithmic Functions are inverses of _______________

Given the above graph of y = 4x, graph y = log4x

What is the domain & range of y = log4x

Given the above graph of y = ex, graph y = ln x

What is the domain & range of y = ln x

Given the above graph of y = log3x, graph y = log3(x+2) – 3

What is the domain & range of y = log3(x+2)–3

Graphing Using TranslationsGive the domain and range & graph each.

1) f(x) = log4(x – 2) + 3

Graphing Using TranslationsGive the domain and range & graph each.

2) y = -logx – 3

Graphing Using TranslationsGive the domain and range & graph each.

3) y = 3 + log2(-x + 1)

Graphing Using TranslationsGive the domain and range & graph each.

4) y = ln(2 – x)

Graphing Using Translations

5)Given the function is a translated

form of y=log3x, find

the equation of the graph.